Integer Factorization: It’s Getting Thrilling (Again)


I am so excited. Yes, I’m struggling mightily to contain that excitement with a large dose of realism – nah, still VERY excited about this. I’m in the midst of programming a new factorization algorithm and Perl script, I’ve finished writing and initially testing the code for calculating some initial values, and will, I hope, code the main algorithm loop tomorrow.

Oh, man.

This has the likely potential to be faster than any integer factorization algorithm I’ve programmed so far. How much faster? I don’t know, and that’s the excitement. The way the algorithm does its job, in theory, is that it takes some calculations based on the odd positive integer that is its argument, creating something I call a Remainder Line through the Cartesian Plane. That line will intersect straight lines I’ve created (and shared earlier) to represent ascending perfect square values. Those lines are boundaries between what I think of as Zones, and what I intend for the algorithm’s main loop to do is jump between those Zones instantaneously, looking for the factorization answer.

Those zones get farther and farther apart in a faster than linear rate. I’m hoping – and this is hope based on a not-yet-tested algorithm – that that approach will jump from one zone boundary to the next INSTANTANEOUSLY – the next iteration is the next Zone line – and because their distance grows rapidly, the algorithm gains speed because it “skips over” candidate values in greater and greater numbers, zeroing in on what I hope is a small set of legitimate candidate values to arrive at an integer point of intersection with a Zone Line and thus give the factorization of the input number.

Yeah, that’s very technical – and I realize my “Integer Factorization” blog posts have been even more technical. But for me, immersed in this idea and finally seeing eleven months of study and scribbled notes and concepts I believe I myself have invented, it’s a thrill ride.

If – and again, I realize this is quite improbable (but, as Zaphod Beeblebrox once explained, not impossible) – this approach is as good as I hope it is, I’ll be jumping to factorization answers more rapidly than I knew possible. It has a tiny chance, in my mind, of meeting the elusive goal of factoring faster than anyone knew possible. And that could jump mathematics into a new era. But that’s only if my inspiration has been very, very good, and I am very, very lucky.

Still, sooooo exciting.

So, the question now remains:

Are you ready for the jump? 😀

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